The trolley problem was largely invented to illustrate why utilitarianism doesn't make sense, why it isn't valid to say something is moral because you're saving five lives while sacrificing one. There's something fundamentally different about pushing a fat man onto the track vs. flipping a switch to divert a trolley, and there's a difference between examining why those two cases are different, and examining why most people agree that those two cases are different. The former is philosophy, the latter seems a bit like someone trying to construct a science of why the people who disagree with them are irrational.